Question

Micah is going to paint his woodworking shop. The shop is a rectangular prism. The dimensions of the shop are shown in the diagram. 15.8 7.9 and 9 Including doors, what is the lateral surface area of the shop in square feet?

Answers: 676.24, 213.3, 426.6,1,23.38

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the lateral surface area of the shop, we need to find the area of the four walls.

The front and back walls have dimensions of 15.8 feet by 9 feet. Therefore, the area of one wall is 15.8 feet * 9 feet = 142.2 square feet.

The two side walls have dimensions of 7.9 feet by 9 feet. Therefore, the area of one wall is 7.9 feet * 9 feet = 71.1 square feet.

Adding up the area of all four walls, we get 142.2 square feet + 142.2 square feet + 71.1 square feet + 71.1 square feet = 426.6 square feet.

Therefore, the lateral surface area of the shop, including doors, is 426.6 square feet.

Answer 2

A pencil holder shaped like a triangular prism is shown. The height of the prism is 12 centimeters.

What is the lateral surface area of the pencil holder in Square Centimeters?

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the lateral surface area of the triangular prism pencil holder, we need to find the area of the three triangular faces.

One of the triangular faces has a base of 12 centimeters and a height of 12 centimeters (the same as the height of the prism). Therefore, the area of one triangular face is (1/2) * 12 centimeters * 12 centimeters = 72 square centimeters.

Since there are three identical triangular faces, the total area of the three triangular faces is 3 * 72 square centimeters = 216 square centimeters.

Therefore, the lateral surface area of the pencil holder is 216 square centimeters.

Answer 4

The other sides are 10 cm and 7 cm

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the lateral surface area of the triangular prism pencil holder, we need to find the area of the three triangular faces.

First, let's find the area of the triangle with sides 12 cm, 10 cm, and 7 cm. We can use Heron's formula to find the area of this triangle:

s = (12 + 10 + 7)/2 = 29/2 = 14.5 cm (semiperimeter)

A = sqrt(s(s-12)(s-10)(s-7))
= sqrt(14.5(14.5-12)(14.5-10)(14.5-7))
= sqrt(14.5 * 2.5 * 4.5 * 7.5)
= sqrt(617.81)
≈ 24.84 cm^2

Since there are three identical triangular faces, the total area of the three triangular faces is 3 * 24.84 cm^2 = 74.52 cm^2.

Therefore, the lateral surface area of the pencil holder is 74.52 square centimeters.

Answer 6

Sides are 10 cm 7 cm and 7 cm

Answer 7

[AI-generated answer — Bot GPT 3.5]

I apologize for the confusion. Since the given sides are 10 cm, 7 cm, and 7 cm, we can calculate the area of the triangle using Heron's formula.

First, let's find the semiperimeter (s):
s = (10 cm + 7 cm + 7 cm) /2 = 12 cm

Next, let's calculate the area (A) of the triangle:
A = sqrt(s(s-10 cm)(s-7 cm)(s-7 cm))
= sqrt(12 cm * (12 cm - 10 cm) * (12 cm - 7 cm) * (12 cm - 7 cm))
= sqrt(12 cm * 2 cm * 5 cm * 5 cm)
= sqrt(1200 cm^2)
= 34.64 cm^2

Since there are three identical triangular faces in the triangular prism, the total lateral surface area is 3 * 34.64 cm^2 = 103.92 cm^2.

Therefore, the lateral surface area of the pencil holder is approximately 103.92 square centimeters.

Answer 8

The sides are 12 cm 10 cm 7 cm and 7 cm

Answer 9

[AI-generated answer — Bot GPT 3.5]

Apologies for the earlier mistake.

Given that the sides of the triangular prism pencil holder are 12 cm, 10 cm, 7 cm, and 7 cm, we can calculate the lateral surface area of the pencil holder.

To calculate the area of the triangular faces, we first need to find the height of the triangular prism. Since the height of the prism is not given, we cannot find the exact lateral surface area.

However, we can calculate the range of possible lateral surface areas based on the given side lengths.

To find the height of the prism, we can use the Pythagorean theorem. The two sides of length 7 cm form the base of the triangle, and the remaining side of length 12 cm is the height.

Using the Pythagorean theorem:
12 cm^2 = 7 cm^2 + h^2
144 cm^2 = 49 cm^2 + h^2
h^2 = 144 cm^2 - 49 cm^2
h^2 = 95 cm^2
h ≈ 9.749 cm (rounded to three decimal places)

Now that we have the height, we can calculate the lateral surface area of the pencil holder.

Area of the triangle with base 12 cm and height 9.749 cm:
(1/2) * 12 cm * 9.749 cm ≈ 58.49 cm^2

Area of the triangle with base 10 cm and height 9.749 cm:
(1/2) * 10 cm * 9.749 cm ≈ 48.745 cm^2

Adding up the areas of the two triangular faces:
58.49 cm^2 + 48.745 cm^2 ≈ 107.235 cm^2

Since there are two identical triangular faces, the total lateral surface area of the pencil holder is approximately 2 * 107.235 cm^2 = 214.47 cm^2.

Therefore, the lateral surface area of the pencil holder is approximately 214.47 square centimeters.

Answer 10

Leigh Ann is designing a wrapper for a new dark chocolate candy bar that her company is going to sell. The candy bar is a

triangular prism. The dimensions of the candy bar are shown in the diagram.
G
E
[
7.4 cm
6.9 cm
7.4 cm
9.9 cm
5.1 cm
Which measurement is closest to the total surface area of the candy bar in square centimeters?

Answer 11

[AI-generated answer — Bot GPT 3.5]

To find the total surface area of the candy bar, we need to find the sum of the areas of all the faces.

The triangular faces have dimensions of 7.4 cm, 6.9 cm, and 9.9 cm. We can use Heron's formula to find the area of each triangle.

Let's start with the triangular face with sides 7.4 cm, 6.9 cm, and 9.9 cm.

First, let's find the semiperimeter (s):
s = (7.4 cm + 6.9 cm + 9.9 cm) / 2 = 12.1 cm

Next, let's calculate the area (A) of the triangle:
A = sqrt(s(s-7.4 cm)(s-6.9 cm)(s-9.9 cm))
= sqrt(12.1 cm * (12.1 cm - 7.4 cm) * (12.1 cm - 6.9 cm) * (12.1 cm - 9.9 cm))
= sqrt(12.1 cm * 4.7 cm * 5.2 cm * 2.2 cm)
≈ sqrt(682.408)
≈ 26.13 cm^2

Since there are two identical triangular faces, the total area of the triangular faces is 2 * 26.13 cm^2 = 52.26 cm^2.

Next, let's find the areas of the rectangular faces.

The dimensions of one rectangular face are 7.4 cm by 9.9 cm, so the area is 7.4 cm * 9.9 cm = 73.26 cm^2.

Since there are two identical rectangular faces, the total area of the rectangular faces is 2 * 73.26 cm^2 = 146.52 cm^2.

Finally, let's find the area of the remaining rectangular face.

The dimensions of the remaining rectangular face are 7.4 cm by 5.1 cm, so the area is 7.4 cm * 5.1 cm = 37.74 cm^2.

Adding up the areas of all the faces, we get 52.26 cm^2 + 146.52 cm^2 + 37.74 cm^2 = 236.52 cm^2.

Therefore, the measurement closest to the total surface area of the candy bar is 236.52 square centimeters.